Usage Surface Deflection Data for Performance Prediction ...

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Usage Surface Deflection Data for Performance Prediction in Flexible Pavement

Nader Karballaeezadeh1, Farah Zaremotekhases2, Narjes Nabipour3, Shahaboddin Shamshirband4,5,*, Amir Mosavi6,7

1 Department of Civil Engineering, Shahrood University of Technology, Shahrood, Iran: [email protected],

2 Department of Construction Management, Louisiana State University, Baton Rouge, LA: [email protected]

3 Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam: [email protected]

4 Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam

5 Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam:

[email protected]

6 Institute of Automation, Kalman Kando Faculty of Electrical Engineering, Obuda University, Budapest, Hungary

7 Institute of Advanced Studies Koszeg, IASK, Koszeg, Hungary

*Corresponding: [email protected]

Abstract

The conventional method used for calculating pavement condition index (PCI) has two major drawbacks: safety problems during

pavement inspection, and human error. This paper proposes a method for removing these problems. The proposed method uses

surface deflection data in falling weight Deflectometer test to estimate PCI. The data used in this study were derived from 236

pavement segments taken from Tehran-Qom freeway in Iran. The data set was analyzed using multi layers perceptron (MLP) and

radial basis function (RBF) neural networks. These neural networks were optimized by levenberg-marquardt (MLP-LM), scaled

conjugate gradient (MLP-SCG), imperialist competitive (RBF-ICA), and genetic (RBF-GA) algorithms. After initial modeling with

four neural networks mentioned, the committee machine intelligent systems (CMIS) method was adopted to combine the results and

improve the accuracy of the modeling. The results of analysis have been verified by the four criteria of average percent relative error

(APRE), average absolute percent relative error (AAPRE), root mean square error (RMSE) and standard error (SD). The best

reported results belonged to CMIS, including APRE=2.3303, AAPRE=11.6768, RMSE=12.0056, and SD=0.0210.

Author keywords: transportation engineering; flexible pavement; pavement condition index prediction; falling weight

Deflectometer; MLP neural network; RBF neural network; Intelligent machine system committee

Introduction

The transportation industry is recognized as the basic infrastructure for economic growth and the development

of other industries throughout the world. The mission of a transportation system is to provide optimal services

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 12 October 2019 doi:10.20944/preprints201910.0141.v1

© 2019 by the author(s). Distributed under a Creative Commons CC BY license.

https://doi.org/10.20944/preprints201910.0141.v1

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to users (drivers, pedestrians, bicyclists or passengers) and thus reduce time and cost of daily lives. In road

transportation, pavement plays a vital role as this part of the road is in direct contact with vehicles and users’

judgement about quality of road service is primarily predicated upon pavement conditions. Therefore,

providing optimal service to users of a road is a function of the proper pavement quality.

Pavement maintenance has attracted growing attention of pavement engineers in recent years. The

Maintenance, Rehabilitation and Reconstruction (MR&R) program is a multidimensional decision-making

process that takes into account several considerations. Highway agencies generally focus on two issues:

maximizing the efficiency of the pavement network or minimizing agency costs(France-Mensah and O’Brien

2019). Both of these issues require the estimation of operating conditions of the pavement network in order to

set up pavement management and maintenance plans.

Detection of pavement surface distresses is essential before setting up a maintenance plan to determine the

pavement operating conditions, as pavement network maintenance operations are arranged based on the state

of such distresses(Suraji, Sudjianto, and Riman 2018). Table 1 shows an instance of pavement network

maintenance operations based on pavement status.

Table 1. Maintenance Program in Roads(Suraji, Sudjianto, and Riman 2018)

Damage (%) Condition Maintenance Program

< 𝟔 Good Routine Maintenance

6-11 Moderate Minor Rehabilitation

11-15 Light Damage Major Rehabilitation

> 𝟏𝟓 Heavy Damage Reconstruction

Given the importance of identifying surface pavement distresses, a variety of distress indices have been

developed by engineers in recent decades. A very common index of the pavement maintenance program is

pavement condition index (PCI), which was developed by the US Army Corps of Engineers in 1982. After

visual inspection of the pavement network, pavement engineers calculate PCI based on the type, severity, and

extent of the distresses. The index varies from zero for a virtually unusable pavement to 100 for an optimal

pavement(Shah et al. 2013).

The process of calculating PCI in a pavement segment involves the visual inspection of pavement. This type

of inspection has always raised safety concerns among engineers. When an inspector is recording surface

pavement distresses, the possibility of clashing into road traffic is relatively high. Another drawback of the



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PCI calculation process is concerned with human error in identifying and recording pavement distress. Human

error can affect the accuracy of calculated PCI. The aforesaid problems underline the necessity of substituting

the current method of PCI calculation with a new one that is bereft of such shortcomings.

In this paper, the authors propose a novel method for estimating PCI in flexible pavements. In the proposed

method, the PCI of a pavement segment can be calculated based on the surface deflections recorded in the

Falling Weight Deflectometer (FWD) testing. FWD is a non-destructive equipment used for pavement

assessment, which provides engineers with useful data including remaining service life of pavement and

overlay thickness by applying impulse loading to the surface of pavement, recording and analyzing

deflections(Karballaeezadeh et al. 2019). Most pavement management systems around the world have FWD

testing in their evaluation programs. Hence, using FWD test results to estimate PCI contributes to the

overlapping and cost-effectiveness of the pavement network maintenance activities. Another major incentive

of the authors was the lack of studies on the link between PCI and pavement surface deflection in the FWD

testing.

To implement the proposed method, the authors selected 236 pavement segments from Tehran-Qom freeway

in Iran. First, PCI was calculated by inspecting all segments and recording surface damage data. Then, all the

segments were subjected to FWD testing and the average deflection of each segment was determined. After

completing the database, multi layers perceptron (MLP) and radial basis function (RBF) neural networks were

used for analysis. The optimization of MLP neural network was conducted by levenberg-marquardt (LM) and

scaled conjugate gradient (SCG) algorithms and RBF neural network was optimized by genetic algorithm (GA)

and imperialist competitive algorithm (ICA) algorithms. Therefore, analytical methods used in this paper are:

MLP-LM, MLP-SCG, RBF-GA and RBF-ICA. Finally, to obtain more accurate results, all four methods were

merged with CMIS in a single model. The results of these five methods were assessed using average percent

relative error (APRE), average absolute percent relative error (AAPRE), root mean aquare error (RMSE) and

standard error (SD) criteria to determine the accuracy of each method. The proposed method enhances the

safety of the PCI determination process by eliminating the field inspection of the pavement. Also, by

removing human factor from the inspection process, the potential human error is eradicated and the accuracy

is boosted.



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This paper is organized as follows. The second section reviews relevant studies in the literature. In the next

section, the research methodology is presented. This section also includes an introduction to PCI and its

calculation method, FWD test, the freeway under study, and data analysis methods. At the end of this section,

the validation criteria of results are presented. The fourth section discusses the results and conclusions are

drawn in the fifth Section.

Literature review

In addition to the conventional method of determining PCI, several other attempts have been made to predict

this index. PCI prediction methods can be broadly divided into three categories:

❖ PCI prediction methods based on other pavement quality indices

❖ PCI prediction methods based on pavement age

❖ PCI prediction methods based on pavement surface deflection

The first category represents the most frequent method used by other researchers. In this category, PCI of a

flexible pavement is determined based on other indices that manifest pavement quality. Surface pavement

distresses have a direct relationship with other indicators of pavement distress, including roughness and

driving quality. Table 2 depicts a number of methods in this category.

Table 2. PCI Prediction Methods Based on Other Pavement Quality Indices

Model Equation Description

Park et al.(Park,

Thomas, and

Wayne Lee 2007)

log(PCI) = 2 − 0.436 log(IRI) IRI: International roughness index.

Dewan and

Smith(Dewan and

Smith 2002) PCI = 153 −

IRI

0.0171 IRI: International roughness index.

Arhin et al.(Arhin

et al. 2015) PCI = (A × IRI) + K + ε

IRI: International roughness index,

A and K: Regression coefficients,

ε: Error

Korea institute of

construction

technology(Suh et

al. 2018)

NHPCI = ((0.004xRD) + (0.003xCR)+ (0.0183xIRI) + 0.33)−2

NHPCI: National highway

pavement condition index,

xRD: Ruth depth(mm),

xCR: Crack ration(%),

xIRI: International roughness

index(m/km).

Korea expressway

corporation

research

institute(Suh et al.

2018)

HPCI = 5 − 0.75RD1.2 − 0.54IRI0.8

− 0.9 log(1 + SD)

HPCI: Highway pavement condition

index,

RD: Ruth depth(mm),

IRI: International roughness

index(m/km),

SD: Surface distress(crack quantity

converted to area)(m2).

Ningyuan et

al.(Ningyuan et al.

2001) PCI = DMI × Ci × √0.1 × RCI × 10

DMI: Distress manifestation index,

Ci: Calibration coefficient for

pavement type,

RCI: Riding comfort index.



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In the second category of PCI prediction methods, researchers focus on pavement age as a major prediction

factor. The pavement age is directly linked to pavement distresses so that different types of damage are more

likely to appear in an old pavement segment. Table 3 reveals examples of methods in this category.

Table 3. PCI Prediction Methods Based on Pavement Age

Model Equation Description

South Dakota

Department of

Transportation(Chen

and Wangdi 1999)

PCI = a + (b × agec)

a: Maximum value of PCI,

Age: Age of pavement(yaer),

b: Slop coefficient of performance curve,

c: Power coefficient for performance

curve.

Oklahoma airfield

pavement management

system(Yuan and

Mooney 2003)

PCI = a0 + a1x + a2x2 + ⋯ + anxn

ai: Polynomial parameters,

x: Pavement age,

n: Polynomial order.

Michles(Michels 2017)

PCI= 71.09 + 27.42(Treatment type)− 4.07(Age)

Treatment type: 0 for microsurfacing and

1 for thin overlay,

Age: Pavement age(year).

The third category of PCI prediction methods involves the pavement surface deflections in the FWD test.

FWD is a device used to evaluate the structural capacity of pavements. The appearance of different types of

surface damage on pavements and their expansion reflects the deterioration of structural capacity of

pavements. Given the above points, there is a mutual relationship between the FWD testing process and

surface distresses of pavement. The paucity of research in this area was one of the reasons prompting the

authors to investigate the relationship between pavement deflection data and PCI index. One of the few

studies that falls into this category of PCI prediction methods is the research undertaken by O'Brein et al.

They developed a model for predicting PCI, which in addition to deflections of surface pavement, drew on

traffic data, pavement age and type of pavement(O'Brien III, Kohn, and Shahin 1983). Eq.1 shows the model

proposed by O'Brein et al.

PCI = 96.6 − [(0.000572 × AGE2 × LPMTOT × DIFF × AREA)

+ (0.3062 × AGE1

4 × AGESOL2 × DIFF2)

+ (0.00156 × AGE1

2 × AGETOT × LPMTOT × DIFF × AREA)]

(1)

where:

AGE: Age of pavement since last overlay (yaer),



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LPMTOT: Log of weighted traffic total (veh/day),

DIFF: Normalized deflection basin slope,

DIFF =D0 − D12

D0

(2)

Di: Pavement surface deflection at i inches from center of loading plate in FWD test,

AREA: Area of FWD deflection basin at the high load level (in.2/103),

AREA = 12(D0 + D12) (3)

AGESOL: Age of pavement to last overlay (year),

AGETOT: Total age of pavement (year).

The data used by O'Brein et al. were obtained from Virginia in the United States. In this study the pavement

surface deflections data were collected using Dynatest 8000 FWD. Statistically, Eq.1 is moderately accurate,

for a correlation coefficient (R2) and a standard error (σ) of 0.586 and 6.88 were obtained,

respectively(O'Brien III, Kohn, and Shahin 1983).

Safety has always been a key factor in transportation engineering. As such, one major strength of the method

proposed in this paper is that it eliminates the need for field inspection of pavement surface distresses, which

significantly promotes the inspection safety. On the other hand, whenever human factor is involved in

scientific processes, the possibility of error induced by inaccuracy and distraction cannot be ruled out. Thus,

the accuracy of PCI estimation process could be improved by eliminating the human factor. Another strength

of this study lies in its application of FWD. Due to its very accurate simulation of traffic load, FWD is a valid

test endorsed by all transportation agencies and is extensively used in many parts of the world for structural

evaluation of pavements. Therefore, the simultaneous use of FWD testing for structural evaluation of the

pavement network and PCI estimation contributes to the overlapping of maintenance activities and diminishes

the consumption budget. The last achievement of this is concerned with its role in filling the research gap in

this area, which could lay the ground for future research in this field.

Methodology

In this section, the methodology of this article is described in detail. The first subsection describes the concept

of PCI and how it is calculated. In the second subsection, FWD is introduced. After introducing the case study



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in the third subsection, the data analysis methods are presented in the fourth subsection. Finally, the validation

criteria for the analytical methods are discussed in the last subsection.

Pavement Condition Index (PCI)

One of the most common indices used to evaluate a flexible pavement is PCI. Introduced by the US Army

Corps of Engineers, this index is based on visuals inspection of pavement(Shahin and Kohn 1981). The PCI

value is a number from 100 to zero, with 100 representing the best pavement conditions and zero indicating

the worst pavement conditions. To calculate PCI in a pavement segment, initially a number of 100 is assigned

to that segment. Then, based on the type, extent and severity of the pavement distresses, a deduct value (DV)

is subtracted from until PCI is finally obtained(Shahnazari et al. 2012). Table 4 shows the relationship

between the pavement status and the value of PCI.

Table 4. Rating Scale of PCI(ASTM 2007)

PCI 0 - 10 10 - 25 25 – 40 40 – 55 55 – 70 70 – 85 85 - 100

Condition Failed Serious Very poor Poor Fair Satisfactory Good

The process of PCI calculation in flexible pavements is summarized as follows(ASTM 2007; Shahin 2005):

1. Determine the type, extent and severity of pavement distresses

2. Determining DV for each distress based on its corresponding curve. Figure 1 shows an example of such

curves.

Fig. 1. Typical deduct value curve(Shahin 2005)

3. Reducing the number of DVs to the maximum number allowed by Eq.4:

mi = 1 +(100 − HDV) × 9

98 (4)

where:



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mi: Maximum allowable number of deduct values,

HDV: Greatest individual deduct value.

4. Determining the number of DVs greater than 2 (q).

5- Determining total deduct value (TDV), which is basically the sum of DVs.

6. Determining corrected deduct value (CDV) based on correction curves using q and TDV. Figure 2 shows an

example of correction curves.

Fig. 2. Typical corrected deduct value curve(Shahin 2005)

7. Decreasing the smallest DVs larger than 2 to 2.

8. Repeating steps 4 to 7 until q reaches 1.

9. Determining the maximum CDV and calculating the PCI using Eq.5:

PCI = 100 − CDVmax (5)

Falling Weight Deflectometer (FWD)

Structural evaluation of the pavement network is one of the requirements of pavement management systems

and FWD is the most common test for structural evaluation of pavement(Levenberg et al. 2018). This test is

widely used by pavement engineers due to the desirable simulation of traffic load. In this experiment, a

loading plate with a radius of 30 cm and 7 to 9 sensors installed at different distances from the center of the

loading plate is placed on the pavement surface. The FWD applies a type of impulsive load to the pavement

surface. To do so, a weight is dropped from a certain height on the loading plate(Karballaeezadeh et al. 2019).

Figure 3 shows the FWD load application system.



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Fig. 3. Loading mechanism in FWD(De Chiara et al. 2012)

After the load is applied to the pavement surface, it generates vertical deflections, which are recorded by the

sensors. Deflection data are transmitted to the central computer for later applications. Useful information such

as remaining service life of pavement, overlay thickness and layers module can be obtained from the

pavement surface deflections(Karballaeezadeh et al. 2019).

Case study

In this paper, 236 pavement segments were taken from Tehran-Qom freeway in Iran to implement the

proposed theory. The study route is part of the artery between the capital and southern Iran, which is located

in two provinces of Tehran and Qom. The freeway consists of 3 lanes in each direction with a width of 3.65 m

for any lane. This freeway has a flexible pavement. A total of 236 pavement segments were selected from this

freeway and the PCI was calculated as described in subsection pavement condition index. After calculating

PCI, a load was applied to the pavement using an FWD equipped with 7 pavement deflection recording

sensors. These sensors recorded the mean deflection in all pavement segments.

Analysis methods

Artificial neural networks constitute a set of computational intelligences inspired by biological neural systems

such as the human brain. Neural networks can be used to explore complex relationships between inputs and

outputs of a system. Each neural network comprises two main elements: the processor elements (neurons and

nodes) that process information, and weights, which are responsible for establishing connections between

neurons(Haykin 2009). The most common artificial neural networks are MLP and RBF, which have been used

in this article.



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Multi-layer Perceptron (MLP) Neural Network

There are three types of layers in MLP. The first layer is the input layer, which is concerned with the input

data. The second type of layer is the output layer that deals with the model output. Between the input and

output layers, there are intermediate layers known as hidden layers. The number of neurons in the input layer

is equal to the number of input variables, while the output is generally the parameter considered for the

analysis. The number of hidden layers and neurons in each hidden layer is determined experimentally.

Generally, a hidden layer is sufficient for most analyses, but in highly complex systems, two hidden layers

could be used. Each neuron in the hidden layer is connected to all the neurons in its preceding and succeeding

layers(Nejad, Mehrabi, and Zakeri 2015). The amount of each neuron in the hidden layer and the output layer

is determined based on the amount of each neuron in the previous layer, weights and bias. To do so, the

amount of each neuron in the previous layer is multiplied by its weight and then the sum of the weighted

values of neurons in the previous layer is obtained and combined with the bias. The obtained value is passed

through an activation function and transferred to the next layer(Nejad, Mehrabi, and Zakeri 2015). Various

activation functions are used in MLP, including Tansig, Linear, Sigmoid and Tanh.

Optimization algorithms used for model training play a key role in MLP performance. In other words, training

optimization in a neural network is equivalent to minimizing a general error function, which is a multivariate

function and depends on weights of the network. In this study, LM and SCG algorithms have been used to

optimize MLP.

The LM algorithm introduced by Kenneth Levenberg and Donald Marquardt is a simple and stable

convergence algorithm, which represents the most prevalent way of optimizing weights and biases in MLP

networks(Yu and Wilamowski 2011). This algorithm is actually a combination of the steepest descent method

and the Gauss-Newton algorithm, which is designed to alleviate computations by excluding the Hessian

matrix(Ranganathan 2004). Interested readers can refer to (Hagan and Menhaj 1994) for further details

regarding the application of the LM algorithm.

Another set of training algorithms for MLP neural networks is the conjugate gradient (CG) algorithms, for

which a variety of algorithms have been presented so far. In conventional CG algorithms, step size is



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estimated using line search technique, which escalates the computational complexity. The SCG algorithm

used in this paper is a CG algorithm that eliminates the line search technique and utilizes a step size scaling

mechanism, thus accelerating the network learning process(Møller 1993; Kişi and Uncuoğlu 2005).

The MLP neural network used in this article has 40 neurons in 4 hidden layers for LM and SCG algorithm.

Tansig, Sigmoid, Tansig, and Tansig sctivation functions, respectively, were used in hidden layers.

Radial Basis Function (RBF) Neural Network

RBF is one of the most popular neural networks introduced by Broomhead and Lowe in 1988. Employed for

both classification and regression purposes, this neural network is inspired by approximation function theory.

The RBF generally has a three-layer feed-forward architecture in which an input layer connects to the output

layer via a hidden layer(Broomhead and Lowe 1988; Sheng 2008). Figure 4 illustrates the structure of the

RBF neural network adopted in this paper.

Fig. 4. Structure of RBF neural network used in this paper

The input layer contains P nodes, where P is the number of model input variables. The main member of the

RBF network is the hidden layer that transfers information from the input to the hidden space. Each point in

the hidden layer is the center of a specific space with known radius(Yildirim and Uzmay 2001). For an input

variable x, RBF network output is calculated as Eq.6(Karim and Adeli 2003):



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y(x) = ∑ wjφj(‖x − cj‖)

N

j=1

(6)

where:

wj: Connection weight,

φj: Radial basis function,

‖x − cj‖: Euclidian distance between input data and radial function center.

In this paper, GA and ICA algorithms are used to optimize the RBF neural network. GA is a meta-heuristic

algorithm inspired by natural selection processes and used for search and optimization problems. In this

algorithm, a set of possible solutions, phenotype, is developed for an optimization problem to find better

solutions. Each person has a set of chromosomes and genotypes that could be modified or stimulated. In this

algorithm, a population of individuals generated in a random process begins to evolve. The fitness (target

function value) of each individual in the population is determined and the fittest individuals are selected to

produce the next generation. The new generation will be used in the next iteration of the algorithm. This

process is sustained until the maximum number of iterations (or the highest number of generations) or the

desired accuracy in the optimization problem is achieved(Davis 1991; Alam, Das, and Pant 2015). Figure 5

shows the GA algorithm.



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Fig. 5. A schematic of GA method in this study

ICA is an algorithm inspired by colonial rivalry, representing an evolutionary algorithm for optimization

problems. This algorithm was first proposed by Atashpaz-Gargari and Lucas. Like other evolutionary

algorithms, ICA begins with an initial population (countries of the world). These countries are split into two

categories of imperialist states and colonies. All colonies are divided among the imperialists in commensurate

with their power and dominance. Each empire consists of an imperialist and a few colonies. The power of

each empire corresponds to the fitness value at the GA algorithm. The power of any empire embraces the

power of the colonial state and its colonies. Over time, the colonies begin to launch a movement against the

imperialists, and some powerful colonies may be able to seize the power of the empire. In the next stage, a

rivalry breaks out between the imperialists with the strong empires gradually growing in strength and the

feeble empires collapsing. The movement of colonies against the imperialists, the rivalry of imperialists, and

the dissolution mechanism continue until all countries merge into one state with only a single empire while

other countries serve as its colonies. Under these conditions, since all colonies are in a relatively identical state



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and they all enjoy the same position and value, the algorithm ends(Atashpaz-Gargari and Lucas 2007;

Hosseini and Al Khaled 2014). Figure 6 shows the flowchart of the ICA algorithm.

Fig. 6. Flowchart of ICA

For GA and ICA algorithms used in this study, the number of neurons and the distribution coefficient were 55

and 0.37, respectively.

Committee Machine Intelligent System (CMIS)

The standard procedure in intelligence analysis is to consider several models for analysis and then select the

best model based on the results. In this process, efforts made for the abandoned models are virtually in vain.

This drawback could be fixed by a committee machine. In a committee machine, the results of different

models are combined to reach a more accurate answer. The important thing in a committee machine is how to

integrate models. In simple arithmetic averaging, all solutions have the same contribution, but in weighted

averaging, the solutions are weighted based on their accuracy and then incorporated into the final

solution(Nilsson 1965; Hashem and Schmeiser 1993; Perrone and Cooper 1992). In this paper, CMIS model

was presented by using MLP-LM, MLP-SCG, RBF-GA, and RBF-ICA neural networks. Weighted

coefficients were optimized by Solver. Table 5 shows the final weighted coefficients in CMIS.

Table 5. Coefficients of CMIS

No. of coefficients Coefficients

C1 0



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C2 0.657295

C3 0.227583

C4 0.069749

C5 0.04656

Performance Criteria

In any scientific study, after analyzing data and calculating the analysis output, the results need to be reviewed

and verified. Four statistical criteria have been used to validate the results in this study including APRE,

AAPRE, RMSE and SD. These criteria are calculated according to the following Eqs. 7 to 10(Hemmati-

Sarapardeh et al. 2018):

APRE =100

N∑

PCIobserved,i − PCIpredicted,i

PCIobserved,i

N

i=1

(7)

AAPRE =100

N∑

|PCIobserved,i − PCIpredicted,i|

PCIobserved,i

N

i=1

(8)

RMSE = √1

N∑(PCIobserved,i − PCIpredicted,i)

2

N

i=1

(9)

SD = √1

N − 1∑ [

PCIobserved,i − PCIpredicted,i

PCIobserved,i

]

2N

i=1

(10)

All the above four statistical criteria represent some kind of computational errors, with smaller values close to

zero indicating higher accuracy of the modeling results. By examining Eqs. 7 to 10, it becomes clear that

APRE can be negative and the other three criteria are always positive.

Results

As mentioned in the previous sections, a set of data derived from Tehran-Qom freeway including PCI and

surface deflection data of pavement, were analyzed using MLP-LM, MLP-SCG, RBF-GA, RBF-ICA and

CMIS methods. The purpose of this analysis was to predict PCI for asphalt pavement based on pavement

surface deflections. These deflections were recorded by seven geophones in the FWD. The FWD applies an

impulsive loading to the pavement surface by dropping a weight on the pavement surface. The resulting

deflections are recorded by one geophone below the loading plate and six other geophones that are 20, 40, 60,



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90, 120 and 150 cm away from the center of the loading plate. Figure 7 shows the relative impact of recorded

PCI deflections. In this figure, D1 to D7 represent the deflections in geophones 1 to 7, respectively. As shown

in Figure 7, geophones 1 to 3 are inversely related while other geophones are directly related to PCI. The

deflections in geophone 7, which is the furthest from the loading spot, wields the highest impact on PCI.

Fig. 7. The relative effect of input parameters on PCI

Table 6 lists the statistical parameters of APRE, AAPRE, RMSE and SD for all the models developed in this

paper. Considering AARPE and APRE values for the CMIS model (11.67% and 2.33%, respectively) and

lower RMSE and SD errors in the CMIS method compared to other models, this model yields the highest

accuracy for predicting PCI among the developed models.

Table 6. Performance Criteria of The All Developed Models for Prediction of PCI Model Data APRE (%) AAPRE (%) RMSE SD

CMIS

Train 3.5636 11.6098 12.0543 0.020082

Test -2.632 11.9464 11.807884 0.025687

Total 2.3303 11.6768 12.005653 0.021081

MLP-LM

Train -1.2093 14.9275 14.541231 0.078995

Test 4.7599 12.7179 14.330003 0.027158

Total -0.02115 14.4877 14.499431 0.068174

MLP-SCG

Train -0.1949 15.5046 14.167214 0.070149

Test 6.6833 13.5662 15.145498 0.031747

Total 1.1742 15.1187 14.367255 0.062318

RBF-GA Train -0.4446 11.8509 13.003455 0.032987

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

D1D2D3D4D5D6D7

Rel

evan

cy F

acto

r



17

Test 14.2997 19.406 58.919147 0.360989

Total 2.4902 13.3547 28.747779 0.096868

RBF-ICA

Train -0.5063 12.6392 17.077364 0.057202

Test 16.7628 25.886 45.214386 0.45286

Total 2.9311 15.276 25.308415 0.134177

According to Figure 8, one can visually analyze the quality of all models developed to predict PCI of asphalt

pavement. In this figure, a graph is presented for all five models proposed in this research. In each graph, the

horizontal axis represents PCIobserved values and the vertical axis represents PCIpredicted values. In Figure 8, the

higher is the data concentration around the Y=X line, the higher is the accuracy of the model in predicting PCI.

As can be seen in this figure, the concentration of points around Y=X line for the CMIS model is higher than

other models, so this model has greater precision in predicting PCI.



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Fig. 8. Cross-plot for developed models to prediction of PCI

Figure 9 reveals the relative error distribution curves. In general, and for each model, the closer the data points

are to the horizontal line of zero error, the greater the accuracy of the model is. According to Figure 9, the

highest relative error between PCIobserved and PCIpredicted in the CMIS model is less than 33%, which is superior

to other models. Thus, Figure 9 also confirms the greater accuracy of the CMIS model compared to other

models.

0

30

60

90

120

0 30 60 90 120

PC

I pre

dic

ted

PCIobserved

MLP-LM

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19

Fig. 9. Relative error between the observed and predicted PCI versus observed PCI

The cumulative frequency curve of AAPRE for models developed in this paper is presented in Figure 10. The

analysis of curves in this figure suggests that the quality of results in models based on RBF neural network is

higher than models based on MLP neural network, especially RBF-GA model, which has a lower error in PCI

prediction. The curve of the CMIS model, which is the median of the results achieved from four MLP-LM,

MLP-SCG, RBF-GA and RBG-ICA methods, lies in the middle of these four methods. However, the end

-80

-60

-40

-20

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point of the CMIS curve is in a better position than all four methods, which corroborates the higher quality of

the CMIS model in PCI prediction.

Fig. 10. Cumulative frequency curve of average absolut relative error for developed models in this study to predict PCI

Conclusion

In this paper, authors attempted to present a method for predicting the performance of flexible pavements. The

most common way to evaluate flexible pavement performance is to adopt an index as an indicator of

pavement performance. In this study, PCI was used as an index of pavement performance. PCI is a numerical

index obtained from the surface pavement distresses and its value is in the range of 0 to 100. A high quality

pavement has a PCI of 100 while a virtually unusable pavement has a PCI of zero. The conventional way to

determine PCI involves inspecting and recording surface distresses of pavement, which suffers from two

major drawbacks: safety risks facing the pavement inspector, and human errors when recording information

and calculations. The method proposed in this paper aims to predict the pavement performance using FWD

test results. The FWD is a non-destructive test used in pavement engineering that assesses pavement by

applying loads identical to the traffic load. The load applied during the FWD test triggers pavement

deflections, which are used as input parameters to predict PCI in this paper. Since FWD is generally used in

pavement network maintenance applications, the method proposed in this paper contributes to the overlapping

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21

of pavement maintenance activities and eliminates the aforesaid shortcomings by abandoning the conventional

PCI calculation method.

To implement the proposed theory in this paper, data set including PCI and pavement surface deflections were

collected based on FWD testing of 236 pavement segments taken from Tehran-Qom freeway in Iran. The data

set was analyzed by two MLP and RBF neural networks. For optimization of MLP neural network, LM and

SCG algorithms were used and also for optimization of RBF neural network both ICA and GA algorithms

were used. To improve the results of four neural networks adopted in this study, CMIS method was employed.

In general, committee machines combine the results of different methods to improve results. The results of

this paper were verified by four statistical criteria including APRE, AAPRE, RMSE and SD, the values of

which in the CMIS method were 2.3303, 11.6768, 12.0056 and 0.0210, respectively.

Given the paucity of studies that have adopted a theory comparable to the one proposed in this paper, this

research is expected to pave the way for future studies in similar areas of research.

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